Question

Use matplotlib to make a cycloid

Please use python

Answer 1

Code in Python:

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation
# Config to put the animation on the jupyter notebook
plt.rcParams['animation.html'] = 'html5'
# radius of the circle
R = 1

def circle(a, b, r):
# (a,b): the center of the circle
# r: the radius of the circle
# T: The number of the segments
T = 100
x, y = [0]*T, [0]*T
for i,theta in enumerate(np.linspace(0,2*np.pi,T)):
x[i] = a + r*np.cos(theta)
y[i] = b + r*np.sin(theta)
return x, y

# Calculate the cycloid line
thetas = np.linspace(0,4*np.pi,100)
cycloid_x = R*(thetas-np.sin(thetas))
cycloid_y = R*(1-np.cos(thetas))
cycloid_c = R*thetas
fig = plt.figure()

lns = []
trans = plt.axes().transAxes
for i in range(len(thetas)):
x,y = circle(cycloid_c[i], R, R)
ln1, = plt.plot(x, y, 'g-', lw=2)
ln2, = plt.plot(cycloid_x[:i+1] ,cycloid_y[:i+1], 'r-', lw=2)
ln3, = plt.plot(cycloid_x[i], cycloid_y[i], 'bo', markersize=4)
ln4, = plt.plot([cycloid_c[i], cycloid_x[i]], [R,cycloid_y[i]], 'y-', lw=2)
tx1 = plt.text(0.05, 0.8, r'$ heta$ = %.2f $pi$' % (thetas[i]/np.pi), transform=trans)
lns.append([ln1,ln2,ln3,ln4,tx1])
plt.xlim(0,15)
plt.ylim(0,3)
plt.xlabel('x')
plt.ylabel('y')
plt.grid()
plt.axes().set_aspect('equal')
ani = animation.ArtistAnimation(fig, lns, interval=50)

ani.save('cycloid_ArtistAnimation.mp4',writer='ffmpeg')
ani.save('cycloid_ArtistAnimation.gif',writer='imagemagick')

ani

Screenshot of the code

import numpy as np import matplotlib.pyplot as plt import matplotlib.animation as animation # Config to put the animation on the jupyter notebook plt.rcParams ['animation.html'-'html5 # radius of the circle R 1 def circle(a, b, r): # (a,b): the center of the circle # r: the radius of the circle # T: The number of the segments T = 100 for i,theta in enumerate(np.linspace(θ,2*np.pǐ,T)): x[i] y[i] r*np. cos (theta) r*np. sin(theta) + a b = + return X, y # Calculate the cycloid line thetas = np.linspace (0,4*np.pi,100) cycloid x R*(thetas-np.sin(thetas)) cycloid y-R*(1-np.cos(thetas)) cycloid_cR*thetas fig = pit. figure()

trans plt.axes().transAxes for i in range(len (thetas)): x,y - circle(cycloid_c[i], R, R) In1, plt.plot (x, y, 'g-,lw-2) 1n2, = pít . plot ( cycloid-x(:1+1] ,cycloid-y [:1+1], 'r-', lw-2 ) ln3, plt.plot (cycloid x[i], cycloid y[i], 'bo', markersize-4) 1n4, -plt . plot ([cycloid-c [1], Cycloid-x [ ї ] ], [R,cycloid-y [1]], 'y-', lw-2 ) tx1 = plt .text ( θ . θ5, θ.8, r'S\theta$-%.2f $\pis. % (thetas [1]/np.pi), transform-trans) Lns.append ([ln1,ln2, ln3, Ln4,tx1]) plt.xlim (0,15) plt.ylim (0,3) plt.xlabel('x') plt.ylabel('y') plt.grid() plt.axes ().set_aspect('equal ani-animation.ArtistAnimation(fig, Ins, interval-50) ani.save('cycloid ArtistAnimation.mp4',writer-'ffmpeg') ani.save('cycloid ArtistAnimation.gif',writer-'imagemagick')

Output:

θ=4.00 π 2 46 8 10 1214

Hope it helps :)